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In mathematical optimization and decision theory, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.

there are a lot of loss functions, such as "squared error loss", "triplet loss"

in the context of grammar, which expression is more appropriate?

  1. Loss functions are important parts of machine learning.
  2. Loss functions is important part of machine learning.

machine learning has a lot of parts, such as objective function, loss function, it seems that expression_2 is more appropriate. i just need a double confirm.

ps:

when I talk about the whole picture of Machine learning, and don't want to go with detail of loss function, should I say "Loss function is an important part of machine learning"?

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(!) Loss functions is important part of machine learning.

This is wrong. The subject of the sentence, "loss functions," is plural: "functions" is the plural of "function". So, the correct subject-verb agreement is:

Loss functions are important parts of machine learning.

If you're talking about a single specific loss function, the singular form is:

A loss function is an important part of machine learning.

Or:

Loss function X is an important part of machine learning.

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